from threading import *
from time import sleep
from sys import stdin,stderr,exit
from copy import copy
from math import log, floor
from random import randrange, choice
from time import time

class Node:
    def __init__(s,neigh,d,initiator=True):

        s.caw=None
        s.rec=0
        s.father=None
        s.lrec=0
        s.win=None
        s.d=d
        s.initiator=initiator
        s.state=['state','sleep']
        s.neigh=neigh
        s.th=Thread(target=s.extinct_echo_center)
        s.id=int(s.th.getName()[7:])-1
        s.num=0
        s.rmsg=None
        s.buffer=[ ]

    def send(s,d,msg):
        d.buffer.append(msg)
    def check(s):
        s.rmsg=s.buffer.pop(0)
        return s.rmsg
    def start(s):
        s.th.start()
    def getName(s):
        return s.id
    def repr (s):
        return str(s.id)
    def add_link(s,z):
        s.neigh.append(z)
    def extinct_echo_center(s):
        addr=dict([(node.id,node) for node in nodes])
        s.num=len(s.neigh)
        if s.initiator:
            s.caw=s.d
            for q in s.neigh:
                s.send(q,('tok', s.d, s.id))
        while s.lrec<s.num:
            sleep(0.01+choice((0.001, 0.002, 0.003)))
            if s.buffer:
                name,r,qid=s.check()
                if name=='ldr':
                    if s.lrec==0:
                        for q in s.neigh:
                            s.send(q,('ldr', r, s.id))
                            s.lrec+=1
                            s.win=r
                else:
                    if r<s.caw:
                        s.caw=r
                        s.rec=0
                        s.father=qid
                        for p in s.neigh:
                            if not p.id==qid:
                                s.send(p,('tok', r, s.id))
                    if r==s.caw:
                        s.rec+=1
                        if s.rec==s.num:
                            if s.caw==s.id:
                                for p in s.neigh:
                                    s.send(p,('ldr',s.d,s.id))
                            else: s.send(addr[s.father],('tok',s.caw,s.id))
            if s.win==s.d:
                s.state='Centre'
            else: s.state='remote'
    n0=Node([ ],4)
    n1=Node([n0],3)
    n2=Node([n1],4)
    n3=Node([n1],3)
    n4=Node([n1,n3],3)
    n5=Node([n4],4)
    n6=Node([n5],5)
    n7=Node([n2],5)
    n0.add_link(n1)
    n1.add_link(n2)
    n1.add_link(n3)
    n1.add_link(n4)
    n2.add_link(n7)
    n3.add_link(n4)
    n4.add_link(n5)
    n5.add_link(n6)
    nodes=[n0,n1,n2,n3,n4,n5,n6,n7]
    for node in nodes: node.start()
    t0=time()
    while 1:
        alive=0
        for node in nodes: alive+=node.th.isAlive()
        print >>stderr,'%d threads alive'%alive
        if alive==0: break
        sleep(1)
    for node in nodes:print node.id,'is',str(node.state)